It will work fine using java script.
<asp:DropDownList ID="DropDownList1" runat="server">
<asp:ListItem>a</asp:ListItem>
<asp:ListItem>b</asp:ListItem>
<asp:ListItem >others</asp:ListItem>
</asp:DropDownList>
<asp:TextBox runat="server" ID="TextBox1" Style="display: none;">
//Download and Add this JS file in your project
http://ajax.googleapis.com/ajax/libs/jquery/1.3.2/jquery.min.js[
^]
// NOw use this script
<script type="text/javascript">
$('#<%= DropDownList1.ClientID %>').change(function () {
if (this.value == 'others') {
$('#<%= TextBox1.ClientID %>').css('display', 'block');
}
else {
$('#<%= TextBox1.ClientID %>').css('display', 'none');
}
});
</script>